STAT 400
Spring 2011
Homework #1
(due Friday, January 28, by 3:00 p.m.)
1.
Suppose that
P
(
A
) = 0.40,
P
(
B
) = 0.30,
P
(
A
∩
B
) = 0.20.
What is the probability that …
a)
either A occurs or B occurs (or both);
b)
B does not occur;
c)
B occurs and A does not occur;
d)
neither A nor B occurs.
2.
Suppose that
P
(
A
) = 0.40,
P
(
B
) = 0.50,
P
(
A
∪
B
) = 0.70.
Find …
a)
P
(
A
∩
B
);
b)
P
(
A
'
∩
B
'
);
c)
P
(
A
'
∪
B
'
).
3.
Suppose
P
(
A
) = 0.6,
P
(
B
) = 0.5,
P
(
C
) = 0.4,
P
(
A
∩
B
) = 0.3,
P
(
A
∩
C
) = 0.2,
P
(
B
∩
C
) = 0.2,
P
(
A
∩
B
∩
C
) = 0.1.
Find …
a)
P
(
A
∪
B
);
b)
P
(
B
∪
C
);
c)
P
(
(
A
∪
B
)
∩
C
'
);
d)
P
(
A
∪
(
B
∩
C
)
).
4.
Let events A and B and sample space S be defined as the following intervals:
S =
{
x
: 0
≤
x
≤
10
},
A =
{
x
: 0 <
x
< 5
},
B =
{
x
: 3
≤
x
≤
7
}.
Characterize the following events:
a)
A
'
b)
A
∩
B
c)
A
∪
B
d)
A
∩
B
'
e)
A
'
∪
B
f)
A
'
∩
B
'
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 Spring '08
 Kim
 Probability, valid probability model

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